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The problem of estimating censored linear regression models with autocorrelated errors arises in many environmental and social studies. The present work proposes a Bayesian approach to estimate censored regression models with AR(p) errors.…
A main difficulty in actuarial claim size modeling is that there is no simple off-the-shelf distribution that simultaneously provides a good distributional model for the main body and the tail of the data. In particular, covariates may have…
In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
Quantile regression (QR) is a statistical tool for distribution-free estimation of conditional quantiles of a target variable given explanatory features. QR is limited by the assumption that the target distribution is univariate and defined…
This paper presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for…
Constrained stochastic nonlinear optimization problems have attracted significant attention for their ability to model complex real-world scenarios in physics, economics, and biology. As datasets continue to grow, online inference methods…
We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…
Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects…
This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…
The standard asymmetric Laplace framework for Bayesian quantile regression (BQR) suffers from a fundamental decision-theoretic misalignment, yielding biased finite-sample estimates, and precludes gradient-based computation due to…
This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of…
Although a number of studies have developed fast geographically weighted regression (GWR) algorithms for large samples, none of them has achieved linear-time estimation, which is considered a requisite for big data analysis in machine…
While covariance matrices have been widely studied in many scientific fields, relatively limited progress has been made on estimating conditional covariances that permits a large covariance matrix to vary with high-dimensional subject-level…
Quantile regression and conditional density estimation can reveal structure that is missed by mean regression, such as multimodality and skewness. In this paper, we introduce a deep learning generative model for joint quantile estimation…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
Coefficient estimation and variable selection in multiple linear regression is routinely done in the (penalized) least squares (LS) framework. The concept of model selection oracle introduced by Fan and Li [J. Amer. Statist. Assoc. 96…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…
The instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2005) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the non-smoothness and…